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The embedding problem for Markov chains with three states

Published online by Cambridge University Press:  24 October 2008

Halina Frydman
Halina Frydman
Affiliation:
New York University
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Extract

In this paper we consider the embedding problem for Markov chains with three states. A non-singular stochastic matrix P is called embeddable if there exists a two-parameter family of stochastic matrices

satisfying

and such that

Though extensive characterizations of embeddable n × n stochastic matrices have been given in (l), (2), (3), (6), and further characterizations of embeddable 3 × 3 stochastic matrices in (4), they do not provide, except in the case of 2 × 2 stochastic matrices, easily applicable necessary and sufficient conditions for embeddability.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 2 , March 1980 , pp. 285 - 294
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

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